# Ultrasonic Monitoring of the Interaction between Cement Matrix and Alkaline Silicate Solution in Self-Healing Systems

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Specimens

#### 2.2. Ultrasonic Testing Configurations

- in the initial state, referred to as “0” (i.e., when the prisms were still intact, before the creation of the transversal crack at mid-span via the initial three-point-bending test);
- in the damaged state, referred to as “1” (i.e., immediately after the generation of the mechanical disconnection at mid-span and before the application of the healing agent on the fracture surface);
- at regular time intervals denoted as “2” to “n”, during the healing process. The first set of measures during healing was taken a few minutes after the healing process has started, and the monitoring procedure continued up to three weeks; though major changes in the acoustic behavior turned out to be established in the first few days, as will be detailed in the following.

- Resonant modes analysis under frequency sweep excitation;
- Linear and nonlinear analysis (transmission coefficients and harmonics generation) under continuous wave excitation;
- Nonlinear analysis according to the Scaling Subtraction Method (SSM) under pulse excitation.

#### 2.3. Ultrasonic Testing Experimental Setup

#### 2.4. Mechanical Testing

## 3. Ultrasonic Tests: Results and Discussion

#### 3.1. Resonant Modes Analysis under Frequency Sweep Excitation

^{®}FFT function (with Blackman windowing and $4\times {10}^{5}$ points, corresponding to the entire duration of the signal). Results are shown in Figure 2, where the evolution of the spectral magnitude with the progression of the healing process is shown for Specimen No. 1. A similar behavior was manifested by the other tested specimens also, but it was not reported here for the sake of brevity.

#### 3.2. Linear and Nonlinear Analysis under Continuous Wave Excitation

#### 3.3. Nonlinear Analysis According to the Scaling Subtraction Method under Pulse Excitation

- exciting the specimens using a sequence of pulses at various amplitudes ${A}_{i}$ in the range 50 mV–15 V (by means of the same equipment described in Section 2.3). More specifically, a rectangular pulse of width $t=10\phantom{\rule{3.33333pt}{0ex}}\mathsf{\mu}$s was used;
- at each time from “2” to “n”, recording the output response ${v}_{i}\left(t\right)$ of the specimen to such a variable-amplitude excitation (in a time window of 10 ms, with a sampling rate of 10 MSa/s);
- calculating the so-called “reference signals” at injection amplitude ${A}_{i}$, defined as ${v}_{ref}\left(t\right)={A}_{i}/{A}_{1}{v}_{1}\left(t\right)$ where ${v}_{1}\left(t\right)$ is the signal detected at the lowest excitation amplitude ${A}_{1}$;
- computing the “scaled-subtracted signals” obtained as the difference in time between the actual output signals at the various excitation amplitudes and the reference signals at the same amplitudes: ${w}_{i}\left(t\right)={v}_{i}\left(t\right)-{v}_{ref}\left(t\right)$; examples are reported in Figure 8;
- summarizing the information contained in the whole temporal signals using compact indicators: in this case, in continuity with [33], the root mean square (RMS) of the signals ($v\left(t\right)$ and $w\left(t\right)$) over a prescribed time interval including only the first arrivals was used. It represents the average power of the signals over the assigned time interval and was denoted as x (RMS of the output signal $v\left(t\right)$) or η (RMS of the scaled-subtracted signal $w\left(t\right)$), while the ratio $\eta /x$ was referred to as y;
- analyzing the relation between y and x and its evolution in time, thus providing information on the type and extent of nonlinearity in the system as a function of the progression of the healing process.

#### 3.4. Discussion

- Immediately after applying the sodium silicate solution, the value of all of the indicators is very close to that of the broken sample;
- After a few days, the healing agent is supposedly almost completely solidified, and the ultrasonic parameters are very close to those measured on the sample in its initial intact state.

## 4. Mechanical Tests: Results and Discussion

## 5. Conclusions

- define a measure of the expected final recovery without the need for a destructive testing;
- speed-up the optimization of the healing agents by sensibly reducing the time needed to assess the recovery in different conditions and for different healing agents;
- define a protocol to ultrasonically monitor the healing process when the healing agent is released from broken capsules, as in real conditions.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Experimental setup: (

**a**) Photograph of the implemented configuration; (

**b**) Sketch of the electronic configuration.

**Figure 2.**Evolution of the output signal spectra as a function of time. Data refer to Specimen No. 1. (

**a**) Spectra at time “0” (intact state, solid black line), time “1” (damaged state, dashed black line) and time “n” (repaired state, solid gray line); (

**b**) Spectra during the healing process, from time “2” to time “n”.

**Figure 3.**Resonance frequency of the first longitudinal mode as a function of time detected with a sweep source. Data refer to Specimen No. 1.

**Figure 5.**Evolution in time of the transmission coefficient T at the fundamental frequency for Specimen No. 1 and Specimen No. 2.

**Figure 6.**Nonlinear effect of second harmonic generation under continuous sine excitation as a function of healing time for Specimen No. 1 and Specimen No. 2.

**Figure 7.**${E}_{NL}={E}_{2\omega}/{E}_{\omega}$ versus ${E}_{\omega}$ for variable-amplitude sine excitations as a function of healing time for Specimen No. 1.

**Figure 8.**Example of reference signal ${v}_{r}ef\left(t\right)$ (black line), detected signal ${v}_{i}\left(t\right)$ (red line) and scaled-subtracted signal ${w}_{i}\left(t\right)$ (green line) in a short time window close to the first arrivals time. Data refer to a sample at an intermediate level of healing and intermediate excitation amplitude ${A}_{i}=12$ V.

**Figure 9.**y versus x plot for variable-amplitude pulse excitations in Scaling Subtraction Method (SSM) experiments at different healing times.

**Figure 10.**Time evolution of the exponent of the power-law fitting used to interpolate the y versus x data from SSM experiments.

**Figure 11.**Load versus deflection curves from three-point-bending tests in the intact state (solid black line) and in the damaged state (solid gray line).

**Figure 12.**Detail of one of the specimens after the final three-point-bending test, with the creation of a new crack path partially separated from the one generated via the first flexural test.

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**MDPI and ACS Style**

Ait Ouarabi, M.; Antonaci, P.; Boubenider, F.; Gliozzi, A.S.; Scalerandi, M.
Ultrasonic Monitoring of the Interaction between Cement Matrix and Alkaline Silicate Solution in Self-Healing Systems. *Materials* **2017**, *10*, 46.
https://doi.org/10.3390/ma10010046

**AMA Style**

Ait Ouarabi M, Antonaci P, Boubenider F, Gliozzi AS, Scalerandi M.
Ultrasonic Monitoring of the Interaction between Cement Matrix and Alkaline Silicate Solution in Self-Healing Systems. *Materials*. 2017; 10(1):46.
https://doi.org/10.3390/ma10010046

**Chicago/Turabian Style**

Ait Ouarabi, Mohand, Paola Antonaci, Fouad Boubenider, Antonio S. Gliozzi, and Marco Scalerandi.
2017. "Ultrasonic Monitoring of the Interaction between Cement Matrix and Alkaline Silicate Solution in Self-Healing Systems" *Materials* 10, no. 1: 46.
https://doi.org/10.3390/ma10010046